Dynamical analysis of a chestnut blight model with two control strategies

Xiaoyu Jin; Shuhe Wang; Longxing Qi; Xiaoyu Jin; Shuhe Wang; Longxing Qi

doi:10.3934/era.2026387

Electronic Research Archive

2026, Volume 34, Issue 12: 9190-9229. doi: 10.3934/era.2026387

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Dynamical analysis of a chestnut blight model with two control strategies

School of Mathematical Science, Anhui University, Hefei 230601, China

Received: 05 July 2026 Revised: 17 October 2026 Accepted: 23 October 2026 Published: 27 October 2026

To investigate how a finite-duration protective intervention interacts with hypovirus-mediated biological control, we formulate a chestnut blight-inspired host–pathogen–hyperparasite model containing susceptible, temporarily protected, pathogen-infected, and hyperparasite-associated host classes. Although no broadly effective and scalable chemical treatment is currently available for chestnut blight, several experimental studies have reported temporary reductions in canker expansion or disease incidence following chemical treatment under specimen-tree, orchard, nursery, or otherwise managed conditions. Motivated by these limited observations, the class $ M $ is interpreted as a temporarily protected class rather than as an immunologically immune class. Susceptible hosts enter this class at rate $ \delta $ and return to the susceptible class after protection is lost at rate $ \rho $. Basic reproduction numbers $ R_{0IS} $ and $ R_{0HS} $ are derived, and the existence and stability of the boundary, disease-free, and positive equilibria are analyzed. We further introduce the composite protection index $ \Theta(\delta, \rho) = 1+\frac{\delta}{\rho+d}, $ which quantifies the combined influence of entry into and loss from the temporarily protected class. Increasing $ \delta $ decreases the effective reproduction numbers and raises the pathogen-invasion thresholds, whereas increasing $ \rho $ has the opposite effect. The parameters $ \delta $ and $ \rho $ also shift the transcritical-bifurcation thresholds associated with hyperparasite invasion and alter the equilibrium distribution among the pathogen-only and hyperparasite-associated classes. Numerical simulations illustrate these threshold shifts and the nonmonotone interaction between temporary protection and hypovirus transmission. The chemical component of the model therefore represents a finite-duration protective effect under idealized conditions, rather than a chemical cure or chemically induced immunity. The results should be interpreted as a theoretical investigation of how temporary protection may affect chestnut blight transmission dynamics, not as a directly validated management prescription for chestnut blight.
- chestnut blight,
- hyperparasitism,
- hypovirulence-associated virus,
- dynamical model,
- transcritical bifurcation,
- control measures
Citation: Xiaoyu Jin, Shuhe Wang, Longxing Qi. Dynamical analysis of a chestnut blight model with two control strategies[J]. Electronic Research Archive, 2026, 34(12): 9190-9229. doi: 10.3934/era.2026387

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Abstract

To investigate how a finite-duration protective intervention interacts with hypovirus-mediated biological control, we formulate a chestnut blight-inspired host–pathogen–hyperparasite model containing susceptible, temporarily protected, pathogen-infected, and hyperparasite-associated host classes. Although no broadly effective and scalable chemical treatment is currently available for chestnut blight, several experimental studies have reported temporary reductions in canker expansion or disease incidence following chemical treatment under specimen-tree, orchard, nursery, or otherwise managed conditions. Motivated by these limited observations, the class $ M $ is interpreted as a temporarily protected class rather than as an immunologically immune class. Susceptible hosts enter this class at rate $ \delta $ and return to the susceptible class after protection is lost at rate $ \rho $. Basic reproduction numbers $ R_{0IS} $ and $ R_{0HS} $ are derived, and the existence and stability of the boundary, disease-free, and positive equilibria are analyzed. We further introduce the composite protection index $ \Theta(\delta, \rho) = 1+\frac{\delta}{\rho+d}, $ which quantifies the combined influence of entry into and loss from the temporarily protected class. Increasing $ \delta $ decreases the effective reproduction numbers and raises the pathogen-invasion thresholds, whereas increasing $ \rho $ has the opposite effect. The parameters $ \delta $ and $ \rho $ also shift the transcritical-bifurcation thresholds associated with hyperparasite invasion and alter the equilibrium distribution among the pathogen-only and hyperparasite-associated classes. Numerical simulations illustrate these threshold shifts and the nonmonotone interaction between temporary protection and hypovirus transmission. The chemical component of the model therefore represents a finite-duration protective effect under idealized conditions, rather than a chemical cure or chemically induced immunity. The results should be interpreted as a theoretical investigation of how temporary protection may affect chestnut blight transmission dynamics, not as a directly validated management prescription for chestnut blight.

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